Can I Close An Email Account And How?

Yes you can. You haven't mentioned which particular account you want to close, so I will tell you about two major ones, i.e, yahoo and hotmail.

To close a hotmail account, you need to take the following easy steps:

After logging into your e-mail account, go into the "Help" link. It's in the top right of your screen. Type "close account" in the search box, then go to the "close yout account link". Follow the instructions on the screen there depending on the kind of account you have ( eg. Paid or free).

To close your yahoo account, you have to think carefully because if you close your e-mail account, you have to say goodbye to all other services that yahoo offers and which you might be using, like flickr etc. That is because you use the same ID and password as your yahoo e-mail for all other yahoo services as well. However, if you still want to go ahead with it, then, here's what you can do.

Go into your yahoo e-mail, and just like with hotmail, look for the "help" link. Which in this case, is also to the right top of your screen. Choose the "account configuration" link under the "Using my Yahoo account" section. There you will find the instructions to close your yahoo account.
  
For both these accounts, it will take some time before they close down. It might take you take about 30 days or so.